In this paper, we consider the following general integral system on the half space ${\mathbb{R}}_{+}^n$ $\left\{\begin{array}{c}u\left(y\right)={\int }_{{\mathbb{R}}_{+}^n}\frac{x_n^{\beta }f\left(v\left(x\right)\right)}{{|x-y|}^{n-\alpha }}dx,y\in \partial {\mathbb{R}}_{+}^n,\hfill \\ v\left(x\right)={\int }_{\partial {\mathbb{R}}_{+}^n}\frac{x_n^{\beta }g\left(u\left(y\right)\right)}{{|x-y|}^{n-\alpha }}dy,x\in {\mathbb{R}}_{+}^n.\hfill \end{array}\right.$Under natural conditions on $f$ and $g$, we obtain a classification of positive solutions by using a slight variant of the method of moving spheres. Some classifications results on the half space were established for $\beta =1$ by Dou, Guo and Zhu (2017) and for general $\beta \ge 0$ by Gluck (2018). These results require a whole integrability hypothesis on $u$ and $v$, which is removed in this paper. Our results thus improve on the classification theorems in Dou, Guo and Zhu (2017), Gluck (2018).

在本文中，我们考虑以下半空间上的一般积分系统 ${\mathbb{[R}}_{+}^{ñ}$ $\left\{\begin{array}{c}ü（ÿ）={\int }_{{\mathbb{[R}}_{+}^{ñ}}\frac{X_{ñ}^{\beta }F（v（X））}{{|X-ÿ|}^{ñ-\alpha }}dX，ÿ\in \partial {\mathbb{[R}}_{+}^{ñ}，\hfill \\ v（X）={\int }_{\partial {\mathbb{[R}}_{+}^{ñ}}\frac{X_{ñ}^{\beta }G（ü（ÿ））}{{|X-ÿ|}^{ñ-\alpha }}dÿ，X\in {\mathbb{[R}}_{+}^{ñ}。\hfill \end{array}\right.$在自然条件下 $F$ 和 $G$，我们使用移动球体方法的细微变化获得了正解的分类。在半空间上建立了一些分类结果，用于$\beta =\mathrm{1个}$ 窦，郭和朱（2017）和一般 $\beta \ge 0$Gluck（2018）。这些结果需要关于$ü$ 和 $v$，已在本文中删除。因此，我们的结果改进了Dou，Guo和Zhu（2017），Gluck（2018）中的分类定理。